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Question

If Pat saved 600ofhisearningslastmonth,howmuchdidPatearnlastmonth?(1)Patspent\frac{1}{2}ofhisearningslastmonthforlivingexpensesandsaved\frac{1}{3}$ of the remainder.
(2) Of his earnings last month, Pat paid twice as much in taxes as he saved.

A
Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
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B
Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
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C
Both statements together are sufficient, but neither statement alone is sufficient.
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D
Each statement alone is sufficient.
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E
Statements (1) and (2) together are not sufficient.
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Solution

The correct option is C Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
Arithmetic Operations with rational numbers
Let E be Pat's earnings last month. Find a unique value for E.
(1) Pat spent 12E for living expenses and so E12E=12E remained. Pat saved 13 what remained, so Pat saved 13(12E)=16E. But Pat saved 600,so600 =\frac{1}{6}E$ and this gives a unique value for E; SUFFICIENT.
(2) Pat saved 600lastmonthandpaid2(600) in taxes, but there is no way to determine Pat's earnings last month; NOT sufficient.
The correct answer is A; statement 1 alone is sufficient.

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